On q-double modified Laplace transform

Abstract

The Laplace transform is widely used in science and technology to deal with complex problemsin stability and control systems. The modified Laplace transform has been applied in physics andmathematics to solve boundary layer equations in ordinary differential equations with variablecoefficients. The q-calculus appeared as a connection between mathematics and physics. It hasmany applications in different mathematical areas, such as number theory, combinatory theory,orthogonal polynomials, essential hyper-geometric functions, quantum mechanics, and relativity.Laplace transform, and its several extended versions are used frequently. The double Laplacetransform applies to solving some q-functional and partial q-differential equations. Q-calculushas been used to solve complex and more potentially typical problems in a larger domain toinvestigate the calculus without limits for getting more generalizations. In the paper, weintroduce the double-modified Laplace transform in q-calculus, namely the q-double modifiedLaplace transform, and establish some properties. Furthermore, several propositions concernedwith q-double modified Laplace transform are explored.

Keywords

• q-calculus
• q-modified laplace transform
• q-integration
• q-differentiation